The　benefits　of　network　coding　in　all-optical　multicast　networks　have　been　widely　demonstrated.　In　this　paper,　we　mainly　discuss　the　multicast　service　efficiently　provisioning　problem　in　the　network　coding　enabled　elastic　optical　networks　(EONs).　Although　most　research　on　routing　and　spectrum　allocation　(RSA)　has　been　widely　studied　in　the　elastic　optical　networks　(EONs),　rare　research　studies　RSA　for　multicast　in　the　network　coding　enabled　EON,　especially　considering　the　time　delay　constraint.　We　propose　an　efficient　heuristic　algorithm,　called　Network　Coding　based　Multicast　Capable-Multipath　Routing　and　Spectrum　Allocation　(NCMC-MRSA)　to　solve　the　multipath　RSA　for　multicast　services　in　the　network　coding　enabled　EON.　The　well-known　layered　graph　approach　is　utilized　for　NCMC-MRSA,　and　two　request　ordering　strategies　are　utilized　for　multiple　multicast　requests.　From　the　simulation　results,　we　observe　that　the　proposed　algorithm　NCMC-MRSA　performs　more　efficient　spectrum　utilization　compared　with　the　benchmark　algorithms.　NCMC-MRSA　utilizing　the　spectrum　request　balancing　(SRB)　ordering　strategy　shows　the　most　efficient　spectrum　utilization　performance　among　other　algorithms　in　most　test　networks.　Note　that　we　also　observe　that　the　efficiency　of　NCMC-MRSA　shows　more　obvious　than　the　benchmark　algorithm　in　large　networks.　We　also　conduct　the　performance　comparisons　of　two　request　ordering　strategies　for　NCMC-MRSA.　Besides,　we　also　evaluate　the　impact　of　the　number　of　the　link-disjoint　parallel　w　paths　on　the　spectrum　utilization　performance　of　the　proposed　algorithm　NCMC-MRSA.　It　is　interesting　to　find　that　the　change　of　the　parameter　w　in　a　certain　range　has　a　significant　impact　on　the　performance　of　NCMC-MRSA.　As　the　parameter　w　increases　to　a　certain　value,　the　performances　of　NCMC-MRSA　cannot　be　affected　by　the　change　of　w　any　more.